理论数学

Vol.3 No.2 (March 2013)

与约数和函数σ(n)有关的一些不等式的解
The Solutions of Some Inequalities of the Sum of Distinct Divisors Function

 

作者:

吴 莉 , 杨仕椿 :阿坝师范高等专科学校数学系

 

关键词:

约数和函数正整数解标准分解式 Sum of Divisors Positive Integer Solution Standard Decomposition

 

摘要:

约数和函数是一类基本而又重要的数论函数。本文推广了由Bencze提出的两个公开问题的结论,证明了对于任意给定的正整数k和非零整数b,均存在无穷多个正整数n,使得以下三个不等式同时成立:,其中为任意正整数n的不同约数之和。

The sum of distinct divisors is a basic and important arithmetical function. In this paper, we extend the conclusions of two open problems proposed by Bencze and prove that, for any given positive integers k and non-zero integers b, there exists infinitely many positive integers n such that the following three inequalities hold simultaneously: , and , where denotes the sum of distinct divisors of n.

文章引用:

吴 莉 , 杨仕椿 (2013) 与约数和函数σ(n)有关的一些不等式的解。 理论数学, 3, 107-111. doi: 10.12677/PM.2013.32017

 

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